Activity Getting a Little Discrete

examples of Discrete Math topics, background information

Assignment Getting There ASAP

Question How Many Moves?

Is it possible to predict the maximum number of moves that can be played in a Sprouts game based on how many vertices at the start of the game?

Activity Analyzing The Game of Sprouts

quantifiable differences, collecting data, looking for patterns, describing patterns

Research Leonard Euler

write 3 sentences about Euler's life and why he is considered one of the greatest mathematicians

Activity The Euler Characteristic

quantifiable differences, looking for patterns

Notes Describing Structures in Graphs

adjacent, planar, complete

Crossword Talking Graph Theory

facts about Euler, graph theory vocabulary

Notes  The "Essence" of a Graph

equivalent representations, isomorphisms, planar

Activity Water Puzzle

draw a graph that represents the game

Research The Four-Color Problem

6 sentences (who, what, where, when, why, how)

Audio Clip Solving or Proving? The 4-Color Problem

Activity Coloring Maps

Four Color Problem, algorithms

Activity Coloring Maps

Four Color Problem, algorithms

Activity Tracing a Graph

Seven Bridges of Königsberg & Eulerian paths, necessary & sufficient conditions

Research The Traveling Salesman Problem

6 sentences (who, what, where, when, why, how)

Notes/Video Movement in Graphs: Paths & Circuits

path, circuit, necessary & sufficient conditions

Notes Traveling Salesman Problem & Algorithms

Nearest Neighbor, Cheapest Link, strategies, establishing simple repeatable steps/clear process

Activity TSP in Florida

find Hamiltonian circuits using the Nearest Neighbor algorithm first then the Cheapest Link algorithm

Review TSP Applications & Algorithms

routing, construction

Read Splitting Terrorist Cells

Discuss Connectivity in Graphs

how to measure, bridges, cut vertices, pieces, applications

Crossword Graph Theory Vocabulary Review

Review Graph Theory Fundamentals

Cheapest Link & Nearest Neighbor algorithms, planar, paths, circuits, complete, adjacent, isomorphic

Sample Test Questions Graph Theory Fundamentals   [Solutions]

Test Graph Theory Fundamentals

Collect Homework & Classwork

Assignment Sudokus - A Glimmer of Algorithms

Discussion Navigating Sudoku Using Algorithms

practice the sudoku algorithm discussed in class

Video/Activity Getting There Efficiently

Dijkstra's Algorithm

Assignment Finding the Shortest Path in Graphs [Numb3rs]

complete questions #1-4

Notes Examining Dijkstra's Byproduct

subgraphs, trees, minimal spanning trees

Activity Modeling: Getting Things Done

flow, directed edges & digraphs, modeling

Assignment Turner Construction

find the least amount of time it will take to complete the construction project

Notes Navigating Flow in Graphs

critical paths, source, sink, quantifying capacity, flow paths & max flow

Assignment Finding the Flow

map the max flow for a digraph

Notes Navigating Flow in Graphs [Numb3rs]

quantifiable differences, starting backwards, exclusionary approach

Assignment How Much Can You Flow?

develop an algorithm to determine the maximum flow in a digraph

Video Applications of Graphs & Algorithms

work flow & queues

Assignment Connecting the Campus

Activity Increasing Electricity Flow

Sample Test Questions More Graph Theory & Algorithms [Solutions]

Test More Graph Theory & Algorithms

Collect Homework & Classwork

Assignment  Is It Prime?

If all you had was a basic calculator, paper, and pencil, explain how you would figure out that 6,887 is not a prime number.

Notes Getting Into Algorithms

multiplication & division, efficiency, prerequisites, Rubik Cubes, divisibility

Research The Sieve of Eratosthenes

Notes Setting the Stage for Number Theory

partitioning & factoring, uniqueness of prime factorization, sifting for primes

Research Goldbach's Conjecture

Who? What? Where? When? Why? How?

Video Getting Primed for Number Theory

distribution of primes, π(n) function, establishing bounds, natural log, comparing quantities

Research Mersenne Primes

Who? What? Where? When? Why? How?

Video Getting to Know Numbers

divisibility, visualizing patterns, proof, Collatz's Question

Research Perfect Numbers & Pentagonal Numbers

Notes Figurative Numbers: Patterns Galore

triangular, square, pentagonal, Gauss & partitions

Research Fibonacci

6 sentences (who, what, where, when, why, how)

Notes Sequences: Gauss & Fibonacci

recursive definitions, partial sums

Activity Generating Sequences in Excel

laptop cart etiquette, basic features

Crossword Number Theory Review

Notes Number Symbols & Zero

recycle vs. create new, place value, alternate base/groupings

Activity Generating Sequences in Excel

Sample Test Questions Number Theory Basics & Algorithms   [Solutions]

Test Number Theory Basics & Algorithms

Collect Homework & Classwork

Assignment Avoiding Friday the 13th

• Is it possible to have a year without a Friday the 13th? Show/explain/justify.

Activity Using Modular Arithmetic: Friday the 13th

modeling repeating cycles, finding congruences

Assignment Predicting the Future

• on a separate sheet, answer #1-9 (must show work)

Notes Into the Mod: Check Digit Applications

algorithms, congruence, ISBN-10 & ISBN-13 numbers

Research UPC Number Check Digits

• similarities & differences from ISBN check digits

Notes/Activity Sneaky Scrambling Algorithms

counting methods, scrambling via modular arithmetic & geometry

Read Cryptography: Secret Writing pp 11-28

• what are the "big ideas"

Notes Only Two Options: Transposition & Substitution

scrambling vs. replacing, algorithms, reversibility

Read Cryptography: Secret Writing  pp 29-56

• be able to discuss/explain at least 2 specific examples

Notes/Activity Going Backwards: Unscrambling

modular arithmetic & inverse operations

Assignment Solving Equations in Modular Arithmetic

Activity Modular Arithmetic Messages

congruence, avoiding negatives, finding remainders

Crossword History of Secret Writing

Activity Going Backwards: Inverses

patterns in modular multiplication/exponents, multiplicative inverses, Fermat & Euler

Test Modular Arithmetic & Introduction to Secret Writing

Collect Homework & Classwork

Read Cryptography: Secret Writing pp 57-90

• be able to discuss/explain at least 2 specific examples & key differences

Notes Mathematics of Substitution: Forwards

methods for scrambling the alphabet, one-to-one correspondence

Read Cryptological Mathematics pp 27-34

• Monoalphabetic Substitution Ciphers

Activity Automating Substitution Ciphers

text & chart referencing functions, number to text conversions, uppercase vs. lowercase

Assignment Monoalphabetic Ciphers

Activity Automating Substitution Ciphers: Generating Alphabets

number to text conversions, replicating patterns using mod

Activity Automating Substitution Ciphers: Affine Shuffles

text & chart referencing functions

Video Code-Breakers: Bletchley Park's Lost Heroes

Quiz Code-Breakers: Bletchley Park's Lost Heroes

Activity Affine Ciphers

additive vs. multiplicative, keys, modular inverses

Read Cryptological Mathematics pp 76-81

• Polyalphabetic Substitution Ciphers

Activity Polyalphabetical Ciphers

keys, modular patterns, Enigma Machine

Assignment Polyalphabetic Ciphers

Notes How Secure Is Your Cipher System?

brute force & key options, strategies for breaking

Read Cryptological Mathematics pp 103-108

• Polygraphic Substitution Ciphers

Notes Increasing Complexity & Subtle Twists

Hill Ciphers/matrix algebra, steganography

Research RSA Encryption

6 sentences (who, what, where, when, why, how)

Notes - Understanding Public Key Encryption: RSA

modular arithmetic, primes, finding inverses, public and private keys

Sample Test Questions Cipher Systems & Spreadsheets  [Selected Solutions]

Test Cipher Systems & Spreadsheets

Collect Classwork & Homework

Assignment Design Your Own Cipher System (example)

• must have substitution and transposition

• not more than 6 steps in complexity

• originality/creativity (5pts max)

• communication/presentation (5pts max)

Cipher System Project - Introduction & Information

scope, expectations, guidelines, specifications

Cipher System Project - Organizational Workday

organize homepage, synthesize ideas for substitution & transposition, establish timeline/key dates, assign responsibilities

Cipher System Project - Computer Workday

enciphering & deciphering spreadsheet designed, initial drafts of PowerPoint presentation & spec sheet

Cipher System Project - Computer Workday

enciphering spreadsheet functional

Cipher System Project - Computer Workday

final versions of PowerPoint presentation & spec sheet completed

Cipher System Project - Computer Workday

deciphering spreadsheet functional,

Notes Overview of Game Theory

quantifying strategies, zero-sum, minimax theorem, Nash Equilibrium

Cipher System Project - Presentations

Activity Two-Player Games: Dr. Markov

Find a Winning Strategy for Saving the Dog

Review Graph Theory

Review Number Theory

Review Cryptography

Course/Teacher Evaluation

Semester Reflection/Final Exam Essay Question

Sample Final Exam